LECTURE 4 - Seismology Hrvoje Tkalčić
Late Professor Bruce A. Bolt (1930-2005) with a model of Chang Heng’s seismoscope
*** N.B. The material presented in these lectures is from the principal textbooks, other books on similar subject, the research and lectures of my colleagues from various universities around the world, my own research, and finally, numerous web sites. Some colleagues to whom I am grateful for the material I used are: B. Bolt, P. Wu, B. Kennett, E. Garnero, E. Calais and D. Dreger. I am thankful to many others who make their research and teaching material available online; sometimes even a single figure or an idea about how to present a subject is a valuable resource. Please note that this PowerPoint presentation is not a complete lecture; it is most likely accompanied by an in-class presentation of main mathematical concepts (on transparencies or blackboard).*** Earthquakes as natural disasters: can we predict them?
San Francisco, 1906 Tokyo-Yokohama, 1923
• Victims in Banda Aceh, Indonesia, after the Sumatra-Andaman earthquake and tsunami in 2004 Pakistan, 2005 Strong motion simulation in SF Bay Area
A simulation of the San Simeon earthquake, CA, through a model of 3D structure. This is achieved using a numerical finite difference method on a grid of points. Berkeley
The main wave front is visibly refracted or bent by contrasts in the velocity across both the Oakland S a n H Hayward and San Andreas a A y faults. n w d a r r e d San a Concentrations of high s amplitude standing waves Francisco persist throughout the movie around San Jose and in San San Jose Pablo Bay. These areas are low- velocity sedimentary basins and cause the amplitudes of ground motion to be amplified as well as extend the duration of the motions. A simulation movie
Both of these factors increase Courtesy of Prof. Douglas Dreger, UC Berkeley and Dr. Shawn Larsen, LLNL the level of hazard to structures. Seismology as a tool for probing the internal structure of the Earth Global shear velocity structure Lithospheric structure under Australia
Li and Romanowicz 1996
van der Hilst, Kennett and Shibutani 1998
Co mpressional Some examples velocity structure in the of seismic lowermost mantle tomography
Tkalčić, Romanowicz and Houy 2002 The beginnings
An artist’s conception of the Chinese scholar Chang Heng contemplating his seismoscope. Balls were held in the dragons’ mouth by lever devices connected to an internal pendulum. The direction of the first main impulse of the ground shaking was reputed to be detected by the particular ball that was released. Early seismographs and advances in seismology
• John Milne - constructed the first reliable seismograph in 1892
• F. Reid - elastic rebound model in 1906 after the Great San Francisco Earthquake and fire Earthquakes happen on preexisting faults
• A notion that the core is needed to explain seismic travel time proposed by R, Oldham in 1906
Emil Wiechert (1861-1928) The 1200 kg Wiechert seismograph for measuring horizontal displacements Probing the Earth with seismology: European discoverers of seismic discontinuities
Andrija Mohorovičić (1857-1936) Beno Gutenberg (1889-1960) Inge Lehmann (1888-1993)
Crust-Mantle boundary 1910 Mantle-Core boundary 1914 Inner Core 1936
Recipe for longevity: study the inner core! The Earth’s Interior
CRUST-MANTLE BOUNDARY Mohorovičić discontinuity (Moho) (1910)
CORE-MANTLE BOUNDARY Discovered by B. Gutenberg (1914)
INNER CORE Discovered by I. Lehmann (1936)
* For Comparison: Pluto discovered in 1931 Berkeley Seismographic Station
•The first seismographs in the western hemisphere installed at the University of California Berkeley campus in 1887 (largely due to the interest of astronomers).
•The occurrence of the San Francisco Great Earthquake and Fire in 1906 began a new era in seismology.
The east-west component of ground motion at the Berkeley station recorded by the Bosch Omori Portion o seismograms recorded by the short-period seismograph on March 10, 1922, from an earthquake vertical-component seismograph at the Jamestown source near Parkfield, California. station of the University of California Berkeley network. The The recording is part of the basis of the "Parkfield wave packet A is the core phase P4KP, and B isP7KP. Prediction Experiment" (1988 ± 5 years). Reproduced on a These exotic seismic phases are multiple reflections from wine label printed for the Centennial Symposium, May the lower side of the core mantle boundary. 28–30, 1987. Seismographs on the Moon
APOLLO 11 APOLLO 14 Astronaut Edwin E. Aldrin Jr., lunar module pilot, is Astronaut Alan B. Shepard Jr., foreground, Apollo 14 photographed during the Apollo 11 extravehicular activity commander, walks toward the Modularized Equipment on the Moon. He has just deployed the Early Apollo Transporter (MET), out of view at right, during the first Scientific Experiments Package (EASEP). In the Apollo 14 extravehicular activity (EVA-1). An EVA checklist foreground is the Passive Seismic Experiment Package is attached to Shepard's left wrist. Astronaut Edgar D. (PSEP); beyond it is the Laser Ranging RetroReflector Mitchell, lunar module pilot, is in the background working (LR-3); in the left background is the black and white lunar at a subpackage of the Apollo Lunar Surface Experiments surface television camera; in the far right background is Package (ALSEP). The cylindrical keg-like object directly the Lunar Module. Astronaut Neil A. Armstrong, under Mitchell's extended left hand is the Passive Seismic commander, took this photograph with a 70mm lunar Experiment (PSE). surface camera. Hooke’s Law of elasticity
When a force is applied to a material, it deforms: stress induces strain – Stress = force per unit area – Strain = change in dimension 1660 Robert Hooke For some materials, displacement is reversible = elastic materials
– Experiments show that displacement is: • Proportional to the force and dimension of the solid • Inversely proportional to the cross-section
– One can write: ΔL ∝ FL/A – Or ΔL/L ∝ F/A – Strain is proportional to stress = Hooke’s law – Hooke’s law: good approximation for many Earth’s materials when ΔL is small Stress and strain
Stress-strain relation:
Elastic domain • Stress-strain relation is linear • Hooke’s law applies
Beyond elastic domain • Initial shape not recovered when stress is removed • Plastic deformation • Eventually stress > strength of material => failure
Failure can occur within the elastic domain = brittle behavior
Strain as a function of time under stress • Elastic = no permanent strain • Plastic = permanent strain
What is the mathematical relation between stress and strain? N ormal strain
x1
The series expansion of u1: S hear strain Stress and strain x2
For small deformations:
The series expansion of u2:
and since u2(A)=0:
x1
Similarly, for AD segment: S hear tensor Dilatation
For products of Δu, Δv, Δw ≈ 0 Stress Stress and strain
Internal traction (stress):
The stress field is the distribution of internal "tractions" that balance a given set of external tractions and body forces.
Stress tensor: σ ij =
σ ij
Direction of the Normal to the surface upon stress component which the stress acts
σ xx = σ 11, σ xy= σ 12 etc. using the notation we used for strain A cubic element in static equilibrium
For a medium to be in stable equilibrium, the moments must sum to zero. Moments are given by the product of a force times the perpendicular distance from the force to a reference point. Let’s consider a As Δx1, Δx2 -> 0, we have σ12= σ21 moment around x3 axis first: Similarly, for the moments around x1 and x2 axes, σ13= σ31 and σ23= σ32. Thus, stress tensor is also symmetric, with 6 independent elements. The most general form of Hooke’s law
ij = Cijkl kl
The constants of proportionality, Cijkl are elastic moduli. We saw that the both strain and stress tensors are second-order tensors, which are symmetric and have 6 independent elements. Cijkl is thus a third-order tensor and in its most general form consists of 81 elements. However, since the strain and stress tensors only have 6 independent elements, the number of
independent elements in Cijkl can be reduced to 36. The first stress eleme nt i s related to the strain elements by:
" ij = C1111#11 + C1112#12 + C1113#13 + C1121#21 + C1122#22 + C1123#23 + C1131#31 + C1132#32 + C1133#33
For an isotropic medium (material properties independent on direction or orientation of sample), the number of elastic moduli can conveniently be reduced to only 2. These elastic moduli are called the Lamé constants λ and µ. !
" ij = #$%ij + 2µ&ij
where δij is Krönecker delta function (δij=0 when i≠j and δij=1 when i=j). This was formulated by Navier in 1821 and Cauchy in 1823.
! Definitions of elastic moduli - from Lay and Wallace book